Things did not go quite as planned. you invested $8,000, part of it in a stock that payed 12% annual interest. However the rest of the money suffered a 5% loss. If the total annual income for both investments was $620.
If $x is invested at 12%, then
.12x - .05(18000-x) = 620
To solve this problem, we need to use the information given.
Let's start by calculating the amount of money that was invested in the stock that paid 12% annual interest. Let's call this amount "x" (in dollars). The remaining amount of money invested, suffering a 5% loss, would then be ($8,000 - x) dollars.
Now, let's calculate the annual income earned from the investment in the stock that paid 12% annual interest. This would be (0.12 * x) dollars.
Next, let's calculate the annual income lost from the remaining investment suffering a 5% loss. This would be (0.05 * ($8,000 - x)) dollars.
According to the given information, the total annual income from both investments was $620. So, we can set up the equation:
(0.12 * x) + (0.05 * ($8,000 - x)) = $620
Now, let's solve this equation to find the value of "x", which represents the amount of money invested in the stock that paid 12% annual interest.
First, distribute 0.05 to ($8,000 - x):
(0.12 * x) + (0.05 * $8,000) - (0.05 * x) = $620
0.12x + 0.40x - 0.05x = $620 - (0.05 * $8,000)
Combine like terms:
0.47x - 0.05x = $620 - $400
0.42x = $220
Divide both sides of the equation by 0.42:
x = $220 / 0.42
x ≈ $523.81
Therefore, approximately $523.81 was invested in the stock that paid 12% annual interest.
To find the amount of money that suffered a 5% loss, we can subtract x from the total invested amount:
$8,000 - $523.81 ≈ $7476.19
Therefore, approximately $7,476.19 was invested in the option that suffered a 5% loss.
To summarize:
- Approximately $523.81 was invested in the stock that paid 12% annual interest.
- Approximately $7,476.19 was invested in the option that suffered a 5% loss.